Abstract
We present a study on the shifted Green biset functors kRF,G of linear F-representations with coefficients over k, for fields k and F of characteristic zero and a finite group G. We provide a criterion for the vanishing of their essential algebras and we prove that the condition of uniqueness of minimal groups for simple modules holds for these functors. We give a parametrization of a family of simple kRQ,G-modules. We also prove the semisimplicity of the category of CRC,G-modules by means of an equivalence with a category of modules over a semisimple algebra.
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